the biggest problem is the 10nm flatness requirement, which is fulfilled by using piezeo actuators and making mated non calibrated surfaces using electroforming
You can approach the flatness with lapping, but the requirement is something like 300 cesium atoms separation. I assume they make something as flat as possible and then use electroforming.
You are right that thermoionic cooling has little use for conventional electronics, but thermotunnel can work at room temperature, if you can set the thing up right. The whole idea is that it can work at room temp.