The NREL solar cell efficiency chart tracks the efficiency of research-level photovoltaics since 1976, and the most up-to-date version is presented below (it was updated in April 2020).
3-J (3-junction) solar cells have seen a steady improvement in efficiency from about 33% in 1999 to 44.4% in 2013, at which point no further research seems to have been done on 3-J solar cells (according to the NREL chart at least). At around the same time, the company Soitec put 4-J cells on the map, the fist one having an efficiency of 44%, followed by a steady increase in efficiency up to 47.1% in 2015. When I say "steady" increase, I mean that the slope we see in the curve for 4-J cells is roughly the same as the slope we see for the 3-J cells from 1999 to 2013, which was excellent progress in increasing solar cell efficiency.
But suddenly it stopped.
- No new reports of progress with 4-J solar cells have been put on the map since 2015.
- No 5-J concentrator solar cells have been put on the map at all.
- One 6-J concentrator solar cell was reported by NREL in the summer of 2019, which was the first 4+ junction concentrator cell reported in 4 years.