Very few isotopes can have "normal" double beta decay (i.e. all the other decays are forbidden).
One of these is 76Ge, so it's possible to have source=detector (using as detector a crystal of Ge, enriched in this isotope, e.g. 86% 76Ge).
It emits two positrons, so the transition is (A,Z)->(A,Z-2).
Criogenics is important in order to see the tiny peak from the annihilation of the positrons.
Stable isotope of Germanium: 68Ge.
It's important to detect the "normal" mode of 76Ge (2β2ν) since this provides the nuclear matrix element for the transition from (A,Z) to (A,Z-2).
"Normal" double beta decay (2β2ν) has been observed (directly, with a TPC) for the first time in 1987.
Main backgrounds: cosmic, and cosmogenic isotopes.
Tracking is important, not only calorimetric measurement of energy, since you also want to suppress the backgrounds.