I grew red, kennebec and russet here in my zone 7 garden. I have raised beds 12" deep. I have never had a potato grow the full 12". Last year I grew some small white potatoes in a bin i made with lattice "wired" together with zip ties. I layered compost and straw and that's what they grew in. Did fine. This year they were fine in the regular raised bins without the "bin". I have also seen potatoes grown in plastic trash cans and specialty potato "grow bags".
After my first taste of homegrown potatoes I vow to grow them every year. They are fantastic and so easy!
i grow them in plastic 5 gal. buckets i puch holes in the bottom for drainage , pour in 2-3 in. of planting mix plant and cover with 2-3 in. more mix , i put 4 potatoes in each one as they grow you pour more mix in untill just the top leaves are showing. whe u harvest all u need to do is tip over the bucket and gather up the potatoes its quick and easy and you can line the buckets up in a sunny spot anywere in the garden. i have gotten high yealds and they dont get bothered by pests