The World powered by the Sun
Today, photovoltaic electricity is only a small fraction of the global electricity production. The volume seems to be one percent in the year 2015. If we do a very simple extrapolation and imagine, that all these PV modules were installed in 2014 and we continue this installation speed, than we need another 99 years, to have a 100% emission free PV world. But this is simply not the way the world goes round.
I will try to extrapolate the situation, based on data from the MIT report "The Future of Solar Energy" 
Analyse the past of Photovoltaic
If we wont to understand the future, it is very useful, to look into the past, not only to understand the development, but also to understand the error which occurred by predicting the future.
The Energy Information Administration (EIA) and the International Energy Agency (IEA) predict since 10 years the global PV installations in a published outlook. The first outlook from 2006 predicted for the year 2030 a global installation of 100 GW. This volume was already matched in the year 2011, only five years after the report was published! Ok, one wrong shot can be excused.
In the year 2011, the EIA predicted 150 GW until 2020. Again a failure, already in 2014 we have reached 180 GW of solar.
The MIT analysed all predictions and compiled them to a very nice picture:
|Figure 1: Different predictions and the reality, source MIT  page 137|
In the early time, the predictions of the IEA had an exponential growth, that is a good guess, because most of the time, new products grow in that type. The only problem was at that time, the growth factor was to small, for example see IEA 2008 prediction in figure 1. Today things have gone worse with the prediction from the IEA. Not only is the factor to small, the prediction includes a reduction of the production of PV itself. This seems hard to understand.(An in depth analysis was done by Christian Breyer, paper PDF)
Things go even more strange, when we look at the price predictions of PV. The EIA predicted the development of the PV price till the year 2030. It should be mentioned, that it is a very difficult task to predict a price of any product for more than 20 years. But this failure is very illuminating.
|Figure 2: Price prediction by EIA IEO 2009 of PV and observed results.  page 137|
Actually, the price even for residential systems dropped to this value already in the year 2014. It should be noted, that the price for residential PV systems in Germany was at the same time at 2$/W.
The price for utility PV systems reached only two years after the report was published the predicted value for 2030, 4$/W.
All this information should be available to the EIA today. It irritates me, why the EIA does not change the prediction about the deployment of PV although they can observe the rapid price drop obviously. (I am thankful for any helpful hint)
Is there enough material for a large roll out of PV
One possible reason, to be pessimistic about the global roll out of PV might be the scare elements used in PV systems. Today almost all PV systems use Silicon to convert sunlight into electricity. The MIT analysed the production of different raw materials, essential for the production of SI-PV-modules.
To set up a PV system we need concrete and steel to mount the panel in the direction of the sun. Glass, aluminium and plastic are necessary to protect the silicon cell, cooper and more plastic is necessary to transport the power away.
|Figure 3: Commodity materials required for PV.  page 131|
Today, all these commodity are produced in a volume, that no real bottle neck will occur. In figure 3, we can see, that the steel production of 9 days is sufficient, to mount all PV panels for 5% of the global electricity production, within half a year, the steel production is sufficient for a 100% conversion to PV.
The least available material in this consideration is glass. For a 100% PV world, we need the glass production of 20 years. But glass production is in no way a limiting factor. The necessary raw material is sand, an endless resource.
The solar cell itself consists of a silicon waver and some silver, are they rare?
|Figure 4: The annual production and requirement for a solar future.  page 135|
In figure 4 we see, that silver might get a little problem, because we need an amount of silver that is produced within 30 years. It should be mentioned that new technologies of production can reduce the necessary mass of silver very strong. Other elements, like Ga are only necessary if we would use GsAs cells in our PV systems what is not widely the case.
We conclude, the raw material is no show stopper for a PV future.
My prediction of PV growth
Compiling all this information, I come to a quite different prediction than the IEA. My simple, but till today best guess is, that the exponential growth will continue, but at a lower rate.
|Figure 5: Long term trend of PV installation.|
In figure 5 we see the global installation of PV shown as a black curve in this logarithmic plot. In the year 1992, we had only 100 MW of PV installed, ten years later, 2002 it was 1000 MW, Today it is about 200 000 MW!
If the growth rate continues at 25%, as seen within the last three years, we will reach 100% PV not long after the year 2030. Remember, today we have a global power plant pool of 5300 000 MW, sufficient to power half the world. Even if we expect, that the future is fair to all people, we need "only" 10 000 000 MW to bring electricity in every home on this planet, long before 2050.
|Update to Figure 5 including the growing power demand, wind and the latest figures available 2016.|
One problem remains: Storage
Without an affordable storage system, PV can only bring electricity during sunny daytime. For a complete conversion, we need about 90 000 GWh of storage .
One solution for residential systems may be the power wall from Tesla, but I am not convinced, that this makes sense on a large scale. For large scale, I recommend the Hydraulic Rock Storage!
References: The Future of Solar Energy, 2015 Massachusetts Institute of Technology, ISBN (978-0-928008-9-8)
 Elon Musk predicts (minute 18) during the presentation of the power wall 90 000 GWh of required storage. https://youtu.be/yKORsrlN-2k