Size quantization in semiconductor particulate films

Optical absorption of polydisperse TiO2: Effect of surface doping by transition metal cations

“…4b is attributed to direct-allowed band transitions. For the undoped anatase, extrapolation of the linear part of the curve (αhν) 2 versus (hν) gives a direct bandgap 3.29 eV, which is very close to the experimental value 3.3 eV found for the anatase single crystals [30], whereas the calculated bandgap value corresponding to the direct interband transition X 1a → C 1b is equal to 3.45 eV [31]. The bandgap values obtained for the direct (E gd ) and indirect (E gi ) transitions for all of our TiO 2 samples are summarised in Table 2.…”

Thermal annealing synthesis of titanium-dioxide nanowire–nanoparticle hetero-structures

“…5. The absorbance data can be related to the optical band gap by using the following relation [39,40]:…”

Synthesis, Characterization and Properties of Zirconium Oxide (ZrO2)-Doped Titanium Oxide (TiO2) Thin Films Obtained via Sol-Gel Process

“…Where C is a constant, Eg the optical band, α is the optical absorption coefficient, hν is the photon energy gap, h the Plank's constant and the exponent n characterizes the nature of band transition; the values of n = 1/2 and 3/2 correspond to direct allowed and direct forbidden transitions, n = 2 and 3 are related to indirect allowed and indirect forbidden transitions [83] and in the cases for a direct band gap semi-conductor like TiO2 the relation become [84,85]:…”