I think for direct allowed transition it should be n =1/2. But very few people used n =2 for direct allowed transition.
Normally is used for indirect band gap 1/2. Here you can see
""For crystalline solids with an indirect band gap, such as rutile TiO2, the dependence of the absorption coefficient k on the frequency ν can be approximated as
equation(13)
khν=A(hν-Eg)2,
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where A is a constant [48]. It is clear from Eq. (13) that the band gap Eg can be obtained by extrapolating to zero a linear fit to a plot of (khv)1/2against hv (often referred to as a Tauc plot)"
For direct band gap is commonly use 2. In the following publications you can find examples how is used. Specially in the source that is the publication from J. Tauc and A. Menth (1972) below.
10.1016/j.solmat.2007.05.005
Article Band-gap determination from diffuse reflectance measurements...
Article States in the Gap
Article Carrier density and interfacial kinetics of mesoporous TiO2 ...
Hi, colleagues! We recently published a new method of spectrophotometric data analysis very similar to the Tauc method but with many advantages over it. In the Tauc method, the main problem is to determine the energy gap without knowing the nature of the optical transition (described with the parameter m). Our method does not require knowledge of the parameter m. The value of energy gap and parameter m can be obtained simultaneously thanks to one linear fit. Other advantages and description of how to use this method are described in the article. We encourage you to read the paper!
Article Inverse logarithmic derivative method for determining the en...
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