birken vs birch

birken is not a noun while birch is a noun.

Word	Noun	Adjective	Verb	Adverb
birken	No	Yes	No	No
birch	Yes	Yes	Yes	No

As adjectives, birken and birch are synonyms defined as:

Other synonyms of birken include birchen.

birken (noun)	birch (noun)
	a switch consisting of a twig or a bundle of twigs from a birch tree; used to hit people as punishment
	any betulaceous tree or shrub of the genus Betula having a thin peeling bark
	hard close-grained wood of any of various birch trees; used especially in furniture and interior finishes and plywood

birken (adjective)	birch (adjective)
consisting of or made of wood of the birch tree	consisting of or made of wood of the birch tree

birken (verb)	birch (verb)
	whip with a birch twig