In terraria, biomes are defined by the blocks that are around. Specifically for desert, you can see on Wiki:
A desert is considered a desert as long as there are at least 1000 sand blocks
However it does not specify the range in which the blocks are being counted. If I were to create a desert by laying the sand on the ground, I need to know how thick the layer must be so that it makes 1000 blocks in the checking range.
If the game checked rectangular area of 1000x1000 blocks the layer would need to be 1 block high.