@Warren, Hi, i'm going to guess that by depth you mean distance from front to back? If so then you're probably familiar with how sound behaves as it moves further away; less bass and less highs with more reflected/reverberant energy.
Feelings of "dimension" in other words "feeling of or sense of space" are essentially linked to the ratio of Early Reflections/Direct Sound. An easy way to hear this is to talk with your hand in front of your face, walk towards a wall whilst talking etc.
How to mimic this? Vocal Centre Panned
Reverb doesn't work, it'll make it too distant sounding.
You need to re-create early reflections appropriate to the size/dimensions of space you want to create.
A wall 6 feet (2m) away will be a 12ft (4m) return journey, approx 1ms per foot {0.3ms/m} means that if you add a delayed version of the sound, 12ms, to the right speaker channel at an appropriate level (try less than -10dB with judicious EQ the sound will begin to "widen"
Tip, do not use identical delay times EQ or volume settings for the left channel otherwise the effect sound will centralise behind the main vocal causing it to recede into the distance.
Some reverbs allow you just to use only the Early Reflections, you may have better luck with this.
Recording Tip I can highly recommend using MS (Mid-Side) for vocal recording. This allows you to add a "flavour" of the room you recorded in.
Re-Recording Tip Send the vocal to a loudspeaker in an appropriate reflective space. Re-record the vocal using MS and a little EQ on the mix.
Regards
James