not exactly sure what you are referring to with escape routes.
There are 2 types, one for take-off/missed approach with an engine inop; the other is for high terrain as crwjerk said, mainly over western China when flying between HKG and Europe and around Alaska where the terrain can be higher than what your aircraft is capable of maintaining engine inop, or if you depressurise. In some high terrain areas there are custom tracks that will fly you down 'valleys' of lower terrain to get you to a nearby airport.
Take-off and go-around engine inop procedures are only sometimes different from the published SID, it all depends on the local terrain for that specific runway.