f-Sum Rule Analysis of the Band Edges in PbS, PbSe, and PbTe

The $f$-sum rule is applied to the conduction- and valence-band edges at the $L$ point in PbS, PbSe, and PbTe. Experimental values of the energy gaps and electron and hole effective masses for PbS and PbSe follow the $f$-sum rule while those for PbTe do not. It is proposed that the well-known anomaly in the relative values of the energy gap of these semiconductors is due to an irregular value for PbTe.