semiconductors

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GaN has just started to be used on high volume mass produced consumer electronics. As example, USB-C chargers with GaN power mosfets are now the default choice for expensive ultrabook computers because they have same size and weight of conventional smartphone chargers. They are also starting to be fitted on high power class-D audio amplifiers.


The latest commercially available power semiconductor is Silicon Carbide (SiC)
https://www.rohm.com/electronics-basics/sic/what-are-sic-semiconductors
They are still expensive but they are gaining popularity on high power DC/DC converters such as EV charging controllers.
 
The gains in the normal stuff have been more on a wafer, finer line widths, changes in fabrication along with reduced supply voltage to reduce power consumption on IC's in particular. Mass sales then make prices fall. It will be the same with parts that use newer materials but it can take a long time. Gains over conventional and sales levels.
 
The state of the art depends on what you are doing. Strained silicon-on-saphire has been quite common for processors for a while I think, for RF/microwave there are lots of options like SiGe, InP, although advanced Si CMOS is making inroads I believe. For high temperature and high voltage power devices SiC and GaN are common now, and for optical there are lots of options (heterojunction devices are common for making optical waveguides that also function as quantum wells allowing efficient LEDs and laser diodes) Silicon is limited in application for optical as its an indirect-bandgap material and cannot complete for efficient light emission as phonons have to become involved - most recombination in Si gives off heat, not light, although there are devious ways round this - dislocation engineered LEDs for instance.