Fairchild F22 was also released 1965, often cited as the first solid state mic as well.I'm interested in this too. Pearl microphones developed TL-4 in the early 70's. It's a very early transformerless (hence the name TL) low noise fet microphone with one amplifier for each side. It had 4mm between the membranes and according to the founder and designer Rune Rosander it didn't have any noticeable phase issues below 8K.
I don't know if it was the first of its kind but Rune was very progressive. In the 50's he developed their rectangular capsules which they still use. Schoeps CMT-20 released in 1965 is often claimed as the first solid state microphone. I have an article about Pearl TC-4 from the same year. KM84 was released in1966 and U87 in 1967.
Both TC-4 and TL-4 are great microphones. Today Pearl also have the DS70, a quad microphone with two capsules mounted on top of each other at an angle of 90 degrees.