Very interesting and significant question. Answer for this question is a billion dollar value and it influences the whole microelectronics world allot in terms of materials abundance, device performance and low cost.
As far as I know to the best of my knowledge we still do not have answer for your question in the literature; but research is going on.
Now let us come to your question how we can address. We can improve sheet resistance by restricting the thickness (as you put limit) only when we can able to improve mobility and carrier density. so think how can you make a super TCO with best mobility and carrier density towards best sheet resistances for thickness less than 50 nm. as of now the practical super TCO is ITO with sheet resistances 10 to 20 ohm per sq. for the thickness's in the range 60 to 80 nm. This is THE ONLY HERO TCO as of now, even though there are many other oxides trying to approach.
If you are interested I am happy to discuss more on this TCO, as I am working in similar topic with CSIRO in Australia and we can plan writing collaborative research proposals and work together to find the Super TCO with superior optoelectronic properties at low thickness... ..
Try playing with defects. We have done the same for MgO and defects change a lot in inducing ferromagnetism, changing optical index and hence transmission and ofcourse, electrical conduction. You can try depositing at elevated temperatures with different partial pressures in PLD or sputtering.
The quality of the conductor oxide film depends greatly on the deposition technique used and on the temperature at which the substrate is maintained during the deposition. In general, more the deposition temperature is high, more the film is conductive; this is due to the formation of oxygen vacancies which give n-type conductivity. Quite the same thing is achieved with a post deposition annealing in vacuum at high temperature (> 400 ° C). Transparency is influenced by the crystalline quality of the film; this also increases by increasing thedeposition temeprature. A good crystalline quality allows a good mobility of the charge carriers, therefore, with the same number of charge carriers a greater conductivity.
The best deposition techniques have proven to be: sputtering (reactive) and PECVD. The so-called wet techniques, whilst giving good films, due to the low deposition temperature, they are not sufficiently conductive if not treated at high temperature.
Deposit a thicker film (or keep on increasing the thickness) till it provides the optical transmission you want (80 ro 90%), and then try to measure the sheet resistance, you can achieve low values.
Recently I have been working on alternative TCO/nanometal/TCO sandwich structure TCO films. It allows obtaining high electrical conductivity as well as the high optical transmission. I submitted the related paper and I will share the full text in near future in here. However, if you like, the following paper will give you an idea about the concept. If you like to fabricate ultrathin TCO layer with high conductivity, I think you should try this method.
All the best.
Conference Paper Spray Pyrolyzed CIS Thin Film Solar Cells Using Sandwich Str...