Question

Strontium titanate ($SrTi{O}_3$) is another wide bandgap semiconductor that has been investigated for use in dyesensitized solar cells. Depending on morphology and pH the conduction band of$SrTi{O}_3$lies around -0.2 V vs. SHE. What energies for the HOMO and LUMO of a sensitizing dye would you specify for electron injection into the conduction band of strontium titanate and for water oxidation by the radical cation formed by photoexcitation?

Short answer

The band gap of the HOMO and LUMO of a sensitizing dye are 1.5 eV.

Step-by-step solution

The given data and the known values.

The conduction band of$SrTi{O}_3$ lies around -0.2 V vs. SHE.

As known;

The standard reduction potential for the${\text{H}}_{\text{2}}|{\text{H}}^{\text{+}}$electrode is 0.000 V.

The standard reduction potential for the${\text{O}}_{\text{2}}|{\text{H}}_{\text{2}}\text{O}$electrode is 1.229 V.

Definition of HOMO and LUMO.

The lower energy level in the chromophore is calledHOMO(highest occupied molecular orbital).

The higher energy level in the chromophore is calledLUMO(lowest unoccupied molecular orbital).

In semiconductors, the highest occupied molecular orbital is called thevalance band(VB), and the lowest unoccupied molecular orbital is called theconduction band(CB).

The band gap of HOMO and LUMO.

The potential of the conduction band ismore negativethan0.0 Vtoreduce${\text{H}}^{\text{+}}$.

The potential of the valence band ismore positivethan1.229 Vtooxidize watermolecules.

Therefore, the reduction potential of the HOMO ismore negativethan the conduction bandstrontium titanate (-0.2 V) to inject electrons, and that of the LUMO ismore positivethan thewater oxidation potential (1.229 V).

Hence, the minimum HOMO-LUMO band gap must be around1.5 eV.