Your best bet is to use gravel board which is about an inch thick, 6 inches
wide and chemically treated. My raised beds are are made of two such boards
the longer sides being attached to 3 X3 inch fence posts at the ends using
coach screws. The shorter sides are likewise screwed to the 3 X 3 which are
inside the corners of the bed.

If you are concerned about leaching chemicals from the wood into the bed,
bear in mind that the inside will be wetter than the outside of the bed so
leaching will not be inwards. Even so, if still worried, paint the inside
of the boards and corners with bitumen paint which is quite cheap and very
effective waterproofingwise!

I have four such beds varying in size from 4 X 4 ft to 8 X 8 which has
asparagus in it.

Geoff