The red pigment vermillion (HgS) is a semiconductor with a band gap of 2.0 eV. It was replaced in the late nineteenth and early twentieth century by CdS_1−xSe_x pigments that are less toxic and more stable. Assuming the band gap follows a linear Vegard’s law type relationship, what composition of CdS_1−xSe_x will have a band gap of 2.00 eV, roughly the equivalent of HgS? See Table 7.8 for the band gaps of CdS and CdSe.

Table 7.8

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Si Ge Elemental semiconductors Bond Band gap distance (A) (eV) 2.35 2.44 Sn 2.81 1.11 (i) 0.67 (1) -0.0 AIP AIAS AlSb GaP GaAs Gasb InP InAs InSb III-V Semiconductors Bond distance () (eV) 2.37 2.45 2.66 2.36 2.45 2.64 2.54 2.62 2.80 Band gap 2.43 (i) 2.16 (1) 1.52 (i) 2.26 (1) 1.43 (d) 0.72 (d) 1.35 (d) 0.36 (d) 0.18 (d) ZnS ZnSe ZnTe CdS* CdSe* CdTe II-VI Semiconductors Bond distance (A) (eV) Band gap 2.34 2.45 2.64 2.52 2.63 2.81 3.6 (d) 2.58 (d) 2.25 (d) 2.42 (d) 1.73 (d) 1.50 (d)