I have an electric sterilizer which my father used in the greenhouse. It's a stainless steel box with metal rods through it which heat up and cook the soil. It kills the beneficials as well as the seeds, but I got tired of raising weeds. You might try putting black plastic down,Any particular trick to sterilizing soil? Weeds are starting to get out of hand on mine too. Carrots especially so since they germinate so slowly.
it works really well for tomatoes and cucumbers. I don't know what to do with the carrots et.al., although once mine come up I'm going to try putting straw down.