>>1090706Check how long the cultivar of carrot you are going to grow gets. Then get a planter that is a few inches deeper than that. Google up, "trough planters" to see what is available and where. What I did with my salad greens for placing under shop lights was to use a salvaged piece of metal to act as a trough. I inlaid plastic, filled them with soil, and planted. It worked out better than expected. Pic related.
If I were to grow carrots indoors and wanted a trough, I'd make one from some wood and line it with plastic. Though, I don't really like using plastic. At least I could get the depth I wanted. A better option is to get into clay pottery and make exactly what you need or make them using Hypertufa. Hypertufa may be exactly what you want for a DIY solution.