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Doping is considered to be the main method for improving the thermoelectricperformance of layered sodium cobaltate (Na$_{1-x}$CoO$_2$). However, in thevast majority of past reports, the equilibrium location of the dopant in theNa$_{1-x}$CoO$_2$'s complex layered lattice has not been confidentlyidentified. Consequently, a universal strategy for choosing a suitable dopantfor enhancing Na$_{1-x}$CoO$_2$'s figure of merit is yet to be established.Here, by examining the formation energy of Gd and Yb dopants inNa$_{0.75}$CoO$_2$ and Na$_{0.50}$CoO$_2$, we demonstrate that in an oxygenpoor environment, Gd and Yb dopants reside in the Na layer while in an oxygenrich environment these dopants replace a Co in CoO$_2$ layer. When at Na layer,Gd and Yb dopants reduce the carrier concentration via electron-holerecombination, simultaneously increasing the Seebeck coefficient ($S$) andreducing electric conductivity ($\sigma$). Na site doping, however, improvesthe thermoelectric power factor (PF) only in Na$_{0.50}$CoO$_2$. When replacinga Co, these dopants reduce $S$ and PF. The results demonstrate howthermoelectric performance critically depends on the synthesis environment thatmust be fine-tuned for achieving any thermoelectric enhancement.

Na Site Doping a Pathway for Enhanced Thermoelectric Performance in $Na_{1-x}CoO_2$; The Case of Gd and Yb Dopants