Energy-Gap Anomaly in the Semiconductor Sequence PbS, PbSe, and PbTe

The f-sum rule has been examined at the conduction- and valence-band edges of PbS, PbSe, and PbTe. Experimental values of electron and hole effective masses, and of energy gaps were used. For both two-band and six-band models, it was found that PbTe does not follow the same f-sum rule as do PbS and PbSe. However, it was also found that, for the III-V and II-VI semiconductor sequences (InSb, InAs, InP), (GaSb, GaAs), and [CdSe, CdS (hexagonal)], the members of each sequence do follow the same f-sum rule. It is concluded that the well-known anomaly in the values of the energy gap EG of the PbX sequence [EG(PbS)>EG(PbTe)>EG(PbSe)] is due to an irregular value of EG for PbTe. It appears likely that this anomalous value of the energy gap of PbTe reflects, through the L₆^- conduction-band edge, an irregular value of the $5s$ electron energy of the tellurium atom. It is proposed that the L₆^- conduction-band edge states in PbTe differ from the equivalent states in PbS and PbSe. This difference results in PbTe having an f-sum matrix element different from that for PbS and PbSe; this is the reason that PbTe does not follow the same f-sum rule as do PbS and PbSe. The f-sum-rule plots of the experimental data for these semiconductors have been used to calculate matrix element values.