Possibility of n-type doping in CaAl$_2$Si$_2$-type Zintl phase compound CaZn$_2X_2$ ($X$ = As, P)

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.