"consisting or made of birch," mid-15c., from birch (n.) + -en (2). Similar formation in German birken.
Entries linking to birchen
birch n.
"hardy, slender northern forest tree noted for its white bark," Old English berc, beorc (also the name of the rune for "b"), from Proto-Germanic *berkjon (source also of Old Saxon birka, Old Norse börk, Danish birk, Swedish and Icelandic björk (which is also a girl's given name), Middle Dutch berke, Dutch berk, Old High German birihha, German Birke).
This is from PIE *bhergo (source also of Ossetian barz, Old Church Slavonic breza, Russian bereza, Lithuanian beržas, Sanskrit bhurjah, all names of birch-like trees, Latin fraxinus "mountain ash"), from root *bhereg- "to shine; bright, white," in reference to the bark. Birch beer is by 1827, American English.
-en 2
suffix added to nouns to produce adjectives meaning "made of, of the nature of" (such as golden, oaken, woolen), corresponding to Latin -anus, -inus, Greek -inos; from Proto-Germanic *-ina- (from PIE *-no-, adjectival suffix).
Common in Old, Middle, and early Modern English: e.g. fyren "on fire; made of fire," rosen "made or consisting of roses," hunden "of dogs, canine," beanen "of beans," baken "baked," breaden "of bread;" Wycliffe has reeden made of or consisting of reeds." The few surviving instances are largely discarded in everyday use, and the simple form of the noun doubles as adjective (gold ring, wool sweater). Some are used in special contexts (brazen, wooden).