Why are elemental dopants for Silicon or Germanium usually chosen from group $XIII$ or group $XV$?

(N/A) When preparing $N$-type or $P$-type semiconductors from pure semiconductors, the size of the impurity atoms should be nearly equal to the size of $Si$ or $Ge$ atoms so that the symmetry of the crystalline structure is maintained before and after the doping process.
Additionally, the type of impurity atoms must be such that after bonding through covalent bonds with the host crystal, the required free charge carriers (electrons or holes) are generated.
These conditions are fulfilled by elements in the $13^{\text{th}}$ (group $XIII$) and $15^{\text{th}}$ (group $XV$) groups of the periodic table, which is why they are selected for preparing $N$-type and $P$-type semiconductors.