We present design studies of a multi-layer PET detector module that uses an 8x8 array of 3 mm square PIN photodiodes to both identify the crystal of interaction and measure the depth of interaction. Each photodiode is coupled to one end of a 3x3x30 mm BGO crystal, with the opposite ends of 64 such crystals attached to a single 1'' square photomultiplier tube that provides a timing signal and energy discrimination. Each BGO crystal is coated with a lossy reflector, so the ratio of light detected in the photodiode and photomultiplier tube depends on the interaction depth in the crystal, and is used to determine this depth of interaction on an event by event basis. A test module with one 3x3x30 mm BGO crystal, one 3 mm square PIN photodiode, and one photomultiplier tube is operated at -20-degrees-C with an amplifier peaking time of 4 mus, and a depth of interaction resolution of 5 to 8 mm fwhm measured. Simulations predict that this virtually eliminates radial elongation in a 60 cm diameter BGO tomograph. The photodiode signal corresponding to 511 keV energy deposit varies linearly with excitation position, ranging from 1250 electrons (e-) at the end closest to the photodiode to 520 e- at the opposite end. The electronic noise is a position independent 330 e- fwhm, so the signal to noise ratio is sufficient to reliably identify the crystal of interaction in a 64 element module.