Planting birch in patio

Does anyone have any experience of planting a tree in a patio? We’re having our patio re done and I want to plant 2 Himalayan birch trees (will be kept pruned to 6m) in a ‘hole’ in the patio. Like the pics attached. They’ll be about 3 to 4 m from the house.
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If you live in Derbyshire, as I do.
Just one further thought though, being a bit keen on a well maintained patio myself, please forgive me for stating the obvious, trees drop leaves, litter and sap and attract wildlife such as birds and squirrels who can spoil your lovely patio!
To maintain them at about 6 metres you will need to employ specialist tree firms which won't come cheap.
A better idea if you're really determined is to plant them in very big planters which might restrict their roots and height.