  Motivated by a recent theoretical suggestion that doping electrons into
various CaAl$_2$Si$_2$-type Zintl phase compounds may give rise to high
thermoelectric performance, we explore the possibility of n-type (electron
carrier) doping of CaZn$_2X_2$ ($X$ = As, P) using first principles
calculation. We consider n-type doping of CaZn$_2X_2$ with the following two
situations: interstitial-site doping of alkaline earth metals $AE$ (= Mg, Ca,
Sr, Ba) and group 3 elements $G3$ (= Sc, Y, La), and $G3$ substitutional doping
for the Ca site. The evaluation of the formation energy of these defects in
various charged states reveals that the interstitial-site doping of $AE$ =
Ca/Mg or $G3$ = Sc/Y, and $G3$ = La/Y substitutional doping for the Ca site are
relatively favorable among the possibilities considered. In particular, the
formation energy of the La substitutional doping for the Ca site is the lowest
among the considered cases both for CaZn$_2X_2$ ($X$ = As, P) and is negative,
which implies that La is expected to be substituted for the Ca site and provide
electron carriers spontaneously. We also find that for each doping case
considered, the formation energy of the defects is smaller for $X$ = As than
for $X$ = P, which suggests that former is relatively easier to realize n-type
doping than the latter.
