> PS: Photovoltaic panels with 20% efficiency are already close to the theoretical limit (see this chapter’s endnotes Current, world record for concentrated solar is 46%.

They are likely referring to the theoretical limit for crystalline silicon based cells (~30% IIRC). This is due to silicon's particular band gap. The record is held by multi-junction cells, which don't suffer from this limitation (which is part of their problem, as they use materials far more expensive than silicon).

I don't think you need to be overly generous when they suggest the UK needs to be both 100% energy independent and 100% free from fossil fuels, and grow 100% of it's food locally, when the UK imports ~35% of it's electricity in 2013 and ~40% of it's food (1). Let alone fossil fuels. And if we can't meet those goals we need to do X.

1: In 2010, the UK produced 73% of ‘indigenous-type foods’, and is about 60% self-sufficient when exports and local consumption are set against production http://www.foodsecurity.ac.uk/food/uk-facts.html

I wasn't arguing for all his calculations, it's just that his evaluation of the theoretical limit of crystalline silicon cells is accurate. He is correct that it is unlikely that they will get much closer to the theoretical limit than 20% in real life situations.

Some GenIV nuclear reactor technologies have a somewhat clearer path to viability than multi-junction solar cells, which have not been able to beat traditional cells in a price-to-performance ratio. We don't even know if there exist materials and processes that can replicate the performance without the costs; see high temperature superconductivity for a technology that's been stuck at that stage for a while, even in the face of the helium shortage.

There are multiple well-attested routes around the Shockley-Quiesser limit most of which do not involve just silicon. One, which MacKay touches upon, is multi-junction systems. Another, which he does not (not being an expert in the field) is via so-called multiple-exciton generation systems. Contrary to most engineers' understanding, this phenomenon is pretty well explained from the point of a low-energy continuum QFT for the materials that most care about for implementation. The real game changer would be to mate these systems with topologically nontrivial materials with surface charge transport protection. Unfortunately with current fabrication capabilities, 70% of the conductivity is in the bulk, which does not possess the topological prohibition to one-particle (or one e-h pair) backscattering. (It would also be interesting to see if the known allowability of 2 particle backscattering applies to excitons in these systems)

Later on on page 44 he changes the assumptions based on 50% efficient farms growing plant matter for biomass. Even if you had 50% efficient panels and you covered 200m^2 per person with them (there are only about 900 m^2 per person that are not covered with farm land or roads), you'd only get about 32KW/person/day which is less than what the energy used for transportation alone (40kw/person/day).

200m^2 at 500w/m2 * 8 hours a day x 20% efficency = 160kwh. Which you could get in the UK using mid range solar cells right now. 50% would get you 400kwh.

Further you can mix solar and wind farms as the wind farm does not take up much space.

Also, he uses mixed units when not realistic. A Tesila roadster for example gets 390 km from a 52kwh battery pack. Doing a direct petroleum has X energy so you need that much electricity is dum as cars have terrable efficency.

But, most importantly the UK already imports a lot of food and energy, making this a really silly comparison. Solar cells in Africa can more cheaply provide energy so that's a better place to put them.