On the Linguistic Turkicization of Azerbaijan, Arran and Sherwan there has not been any detailed study (for example a book or a Ph.D. Thesis) as far as I know. The work of Kasravi although a good start needs much more work since much new evidence has been unearthed since his demise.
Three drawbacks I have seen with regards to currents studies are:
Authors have lumped Azerbaijan, Arran and Sherwan together although Turkicization occurred differently and at different pace in these areas.
Authors have not distinguished between nomadic plains (say the Mughan steppes) and urban city centers. It takes many generation to give up the nomadic lifestyle, for semi-nomadic lifestyle, to rural settlements and finally to urban settlement.
Authors have not looked in detail at the differences of Islamic sects. For example in Western Iran unlike Khorasan, the population was mainly Shafiâi where-as the Turks that entered the region were overwhelmingly Hanafi.
This study is not a complete study but it sheds light on sources that scholars have overlooked. For example our main concern are the linguistic Turkicization of the Muslims of the area. It also uses the three above points to study the linguistic Turkicization of Azerbaijan in detail. Finally, we take a look at some arguments in the Appendix that carry no weight but have been promogulated for non-scientific reasons. Overall the study shows that until the Safavid period, the Turkicization of Azerbaijan and Sherwan were far from complete. Some other authors have mentioned that Turkification was near complete near the end of the Seljuq or Mongol era, but direct evidence provided here contradicts them. On Arran we have less data after the Mongol period although an important manuscript is brought to light. What this study does highlight is important manuscripts that have been neglected that shed light upon the the linguistic Turkicization of Azerbaijan, Arran and Sherwan.
These notes are mainly concerned with the linguist shift of the Muslim population from Iranian to Turkic languages.