eGaN transistors are very similar to lateral FETs (Field Effect Transistors) made in silicon. Please refer to the application note Fundamentals of Gallium Nitride Power Transistors for a general discussion of the devices and technology.
The following videos also cover the basics of GaN:
How To GaN 01: Introduction – Material Compositions
How to GaN 03 – Performance Characteristics
EPC’s GaN Power Transistor Structure
Scanning electron micrograph cross section of an eGaN FET